HSC Arts इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Solve the following differential equation:

`(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x` = 0, given that y = 0 when x = 1

Solve the following differential equation:

(x² + y²) dy = xy dx. It is given that y (1) = y(x₀) = e. Find the value of x₀

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The solution of `("d"y)/("d"x) + "p"(x)y = 0` is

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The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is

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The solution of `("d"y)/("d"x) = 2^(y - x)` is

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The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is

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If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is

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The number of arbitrary constants in the general solutions of order n and n +1are respectively

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The number of arbitrary constants in the particular solution of a differential equation of third order is

Compute P(X = k) for the binomial distribution, B(n, p) where

n = 6, p = `1/3`, k = 3

Compute P(X = k) for the binomial distribution, B(n, p) where

n = 10, p = `1/5`, k = 4

Compute P(X = k) for the binomial distribution, B(n, p) where

n = 9, p = `1/2`, k = 7

The probability that Mr.Q hits a target at any trial is `1/4`. Suppose he tries at the target 10 times. Find the probability that he hits the target exactly 4 times

The probability that Mr.Q hits a target at any trial is `1/4`. Suppose he tries at the target 10 times. Find the probability that he hits the target at least one time

Using binomial distribution find the mean and variance of X for the following experiments.

A fair coin is tossed 100 times, and X denote the number of heads

Using binomial distribution find the mean and variance of X for the following experiments.

A fair die is tossed 240 times and X denotes the number of times that four appeared

The probability that a certain kind of component will survive a electrical test is `3/4`. Find the probability that exactly 3 of the 5 components tested survive

A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be at least one defective item

A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be exactly two defective items?

If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights exactly 10 will have a useful life of at least 600 hours